This analysis is made as part of Udacity’s Data Analyst Nanodegree Project 6.

Prosper is a website that connects borrowers and lenders directly. There are no financial intermediaries. Each borrower gets a rating with a letter that tells the risk of that loan. With AA being the highest rating and HR (High Risk) being the worst type of rating. Also we can see there are some other variables of interest such as the APR on that loan, the amount or the category. This data set contains 113,937 loans with 81 variables on each loan, including loan amount, borrower rate (or interest rate), current loan status, borrower income, borrower employment status, borrower credit history, and the latest payment information. I’ll try to analyze and summarize all this information using R.

Univariate and Bivariate Plots Section

We will start by analyzing some key variables when taking a loan like borrower APR, principal amount, credit score, loan status and more.

1st, let’s look at how the borrower annual percentage rate is distributed across all loans. This tell us how expensive it is to seek funding in Prosper.

Hm… interesting, we see that the distribution spikes at about 0.21 but then spikes 2 more times at 0.3 and 0.36. It’d be interesting to analyze why this happens.

We can see below how the borrower’s APR distributes across Credit Rating, which determines the risk level of the borrower. As this risk level decreases (score goes up closer to AA) the rate at which the borrower finances seems to decrease. This seems to explain why we see the spike in the total distribution of the APR. Contrary case, as the credit rating score decreases, interest rate goes up.

We can really appreciate in the above graph how the APR raises as Credit Rating gets lower. Below is the distribution for each rating

## ld$CreditRating: AA
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## 0.01650 0.08325 0.09142 0.09645 0.10140 0.33172 
## ------------------------------------------------------------ 
## ld$CreditRating: A
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## 0.01315 0.12461 0.13734 0.13841 0.15077 0.36623 
## ------------------------------------------------------------ 
## ld$CreditRating: B
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## 0.01325 0.16653 0.17754 0.17985 0.19501 0.37633 
## ------------------------------------------------------------ 
## ld$CreditRating: C
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## 0.00653 0.20040 0.22108 0.21866 0.24205 0.40243 
## ------------------------------------------------------------ 
## ld$CreditRating: D
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## 0.00653 0.24614 0.27467 0.26626 0.29510 0.41355 
## ------------------------------------------------------------ 
## ld$CreditRating: E
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## 0.01657 0.30131 0.32446 0.31589 0.34621 0.41355 
## ------------------------------------------------------------ 
## ld$CreditRating: HR
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## 0.00864 0.30564 0.35643 0.32794 0.35797 0.42395

Let’s move on to analyze how much money borrowers request when asking for a loan on Prosper.

We see most loans are below $ 5,000, although we see other spikes in the $10,000s and the $ 15,000s. This may be related to the psychological factor of being $ 5,000 multiples, and people like this kind of numbers, and they don’t request the exact amount they need, but round up to a 5000 multiple.

On the above graph, we’ve faceted the borrowed amount by category. We can see that the categories that borrows the biggest amount are Debt Consolidation, Home Improvement and Business.

Moving on, let’s see how the term of the loans distribute. It’s interesting to see for how much time borrowers will need the money.

So we can see above that only 3 term values appear, this may be due to a limitation of Prosper to only offer 3 terms when borrowing a loan. We also see that the value that appears the most is the 36 months term (3 years) The max value is 60 months (5 years), the minimum 12 months (1 year).

Let’s continue with analyzing the Credit Score distribution of each borrower, this may tell us if people with bad credit score use Prosper more than people with good credit score.

We see that the credit score follows a pretty normal distribution with most values in the 650-700 range. Although we see some outliers especially in the low end. We can also see a small spike in the 500-550 range.

Let’s now analyze the stated monthly income of the borrowers.

We can see from the above graph that the distribution is right-skewed as most of the values are at the left and we see less extreme values to the right. This makes sense as we don’t expect that people with a lot of income to have the need to borrow money.

Let’s now see what’s the average monthly loan payment.

We can see above how much it is paid per month on each of the loans, we see the distribution really spikes in the $150 monthly payment.

Based on both variables looked above, let’s move on now to, what I believe it is one of the most important variables when analyzing if you should give a loan to someone. The Debt Income Ratio calculates how much of debt services you have to pay each month, divided by your monthly income, as it is closer to one, the more indebted you are and the more difficulties you are going to have when repaying a loan. Let’s see how this variable distributes across our dataset.

So we see a very extreme value of almost 10 in the far right. This value makes no sense as it means someone pays 10 times per month of their monthly income! Let’s limit the graph so we see the distrbution of the left-sided values. We can also see that most values are below one, which makes total sense as it is very difficult for someone to survive paying each month more of what it earns.

Now we can see a nice distribution of the debt to income ratio, with most values in the 0.15-0.20 range, which also makes sense as it is normal that someone spends 15-20% of their income in servicing their debts.

Let’s take the analysis even further and see if there is any difference on the ratio based on Credit Rating.

Let’s look now at the time it takes to get a loan from the date you create a listing.

We can see in the graph above that most listings get a loan in 3 to 10 days. We see that the distribution is right-skewed as most values are to the left of the distribution, with more extreme values to the right. It looks that you can get a loan pretty fast in Prosper, with exception of some cases. And also it is filled with the Credit Rating and it seems the Credit Rating doesn’t have an impact in how fast you can get a loan.

Let’s move on now to some categorical variables. Let’s start with the Credit Rating. We can see below how the borrwoers distribute accross Credit Rating. We see most of them tend to have a medium credit rating (C) and more extreme values (AA and HR) are rarer.

Let’s look at the distribution of Credit Ratings by Category.

It’s interesting to see that the borrowers that ask for a loan for Cosmetic Procedures are rated as HR. On the other side, most of the borrowers in Category Boat are high-rated.

Let’s go with another categorical variable like the states of the borrowers, so we can see the distribution across states.

We can see from the above that the borrowers are mainly from California, Florida, Texas and New York. This may have to do with the amount of population in each of these states, as these 4 states account for 30% of the total of US population.

Let’s now look at the Loan Status of each loan.

We can see most loans are active (current), then completed and lastly charged off. We see a small amount of loans are past due.

Quantitative vs Quantitative

Let’s start with looking at the relationship with Credit Score and Borrower’s APR.

## 
##  Pearson's product-moment correlation
## 
## data:  ld$CreditScore and ld$BorrowerAPR
## t = -172.37, df = 113080, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.4607567 -0.4515253
## sample estimates:
##        cor 
## -0.4561533

We can see from the above graph that there seems to be a negative medium correlation between the credit score of the borrower and the APR it is charged for the loan. This is, as the credit score increases, the lower the borrower will be charged for the loan. This is only based on the correlation but remember that correlation does not mean causation. I’ve also added transparency to the points so that we can see were most of the values concentrate. Also the Y axis was log-transformed so we can more clearly see the change in the APR as the Credit Score increases.

Let’s now look to at the relationship between credit score and the principal amount borrowed.

## 
##  Pearson's product-moment correlation
## 
## data:  ld$CreditScore and ld$LoanOriginalAmount
## t = 126.67, df = 113080, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.3473921 0.3576005
## sample estimates:
##       cor 
## 0.3525068

So at 1st sight we can see some kind of increase in the amount lended as the credit score increases. Let’s transform the y-axis to see if we get a more clear relation. We also see these horizontal bars in the $5,000 multiples, which goes in line with what we saw in the histogram of the Loan Amount, where people usually borrows these amounts due to a psychological factor of the number.

We can see a weak relationship between these 2 variables with a lot of spread, but this has to do mainly with that a borrower with a high credit score does not necesarily asks for a high amount of principal. Anyway, we can see that borrowers with low credit score have no loans with high principal.

Qualitative vs Quantitative

Let’s now move to some relationships between qualitative and quantitative variables. Let’s start with seeing the relationship between credit rating and borrower’s APR. We’ve already peaked this relationship on the histogram of the APR, filled by Credit Rating. And above looking the relation between Credit Score and APR.

So it can be cleary see from the above graph that as the credit rating gets worse, the APR for the loan is higher. We can see a lot of outliers anyway for both extremes (AA and HR). We also see how the IQR increases as the rating gets worse, this may be due to a factor of “luck” in getting a better rate for worst rated borrowers. We’ve added alpha to the outliers to show that they are not the norm and are rather unusual.

Let’s take the above further and divide also by the term of the loan.

We can see that for the best ratings as the term of the loan increases, so does the rate. This has to do with the risk of lending to longer terms, mainly the risk of interest rates rising. The same doesn’t apply very much to lower rated borrowers.

let’s now look at the relationship between Credit Rating and Monthly Income.

We can see that the monthly income tends to decrease together with the rating. This has makes sense as it could be that lower income people, struggle more with debt, which lowers their rating.

Let’s continue with the credit rating and now let’s compare it to the amount borrowed.

Very interesting graph. We clearly see a difference in the amount borrowed by lower rating people. Could this be due to an aversion from the lenders to lend to bad rated borrowers, or a precaution from the borrower to not ask for something he/she won’t be able to repay. It’s also clearly seen how until rating C the IQR are quite wide and reaches an amount of almost 15,000, but then that values decreases significantly, together with the rating.

The next one is pretty obvious but it’s worth seeing it anyway. It shows the relationship between credit rating and credit score.

So the above graph is what we expected to see. A lower credit score is related with a lower rating. It is worth noting the IQR of the HR Rating, it is much wider than the other ratings, and even the median is higher than E rating, which is weird.

Let’s try to see where does the bad rating comes from. To do that we are now seeing the Credit Rating vs Delinquencies in Last 7 years.

And voila. Here is from where the bad rating comes from. We can cleary appreciate how for the best rated borrowers the IQR is almost null (no delinquencies), but as we get down the rating, we see the the IQR starts to increase and we see it is more normal for lowest rated borrowers to have at least 1 delinquency in the last 7 years.

Let’s continue with analyzing the differences between the ratings. Now its the turn of the total enquiries.

So based on the above graph we can see that inquiries increase as rating gets worse. This may be related to the fact that people that got to a bad credit rating in the 1st place was because of little or none personal finance education, so that’s why more inquiries are made. That’s why so important to have a solid base in personal finance education.

I think it was enough of the Credit Rating variable. Let’s now move on to see some information about the Loan Categories.

We can see from the above that some categories have a lot of variability in the amount borrowed, such as Debt Consolidation, Baby/Adoption and Wedding Loans. Also the category with the highest median is Debt Consolidation with a value of almost 10,000. In the other extreme we have the lower variability categories, such as Student Use, Personal Loans and Household expenses. With the Student category having a median value of about 2,500.

Multivariate Plots Section

Let’s now plot together our main variables, APR, Principal and the Rating.

The above graph confirms what we’ve been seeing before. As The lowest APRs are for the highest rated borrowers (dark green strip) and as rating gets worst, so does the APR. It is also interesting to see that the loan amounts are also affected by the rating. The loans of $ 30,000 or more only go to borrowers with at least B rating.

Final Plots and Summary

Plot One

Description One

The above graph is a simple histogram, but adding the coloring by Credit Rating gives us so much information. It is our start of the exploration of how this variables, APR and Rating, affect a loan. It is clearly seen how the distribution changes together with the Rating. We can see that worst rated borrowers are more to the right side of the graphic as that means a higher APR, due to the increased risk.

Plot Two

Description Two

The above was surprising for me as it is clearly seen how lowest rated borrwers don’t get big loans, instead the loan is well below the 5,000 limit. It is interesting to investigate if this is an aversion from lenders to borrow high- risk borrowers. Or a precaution from borrowers to not ask more than they are capable of repaying.

Plot Three

Description Three

For the last graph I chose one that merges the above 2 and let us see the whole picture. We can see these colores “strips” across the graph, that divide the borrwers based on its credit rating. As these strips go higher the APR increases, so it is no surprise that HR category is at the top. We can also see some kind of vertical strips across the amount loaned in the $5,000 multiples. And also how only high rating borrowers are given big loans.

Reflection

I was very interested in finding what made the different APRs for the loans. And I was not surprised to find out that these loans follow one of the most basic finance principles, as risk increases so does return, which in this case is expressed with the APR. One of main struggles I had was dealing with so many variables and knowing which one were useful and which ones not. Overall it is a very interesting data set, for which I wish I have more time to investigate it more thoroughly. It would be interesting to analyze the evolution of loans over time and how the APR varies together with US Fed rates.